A sampling theorem for deconvolution of point sources

Brett Bernstein, Carlos Fernandez-Granda

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

We study the problem of recovering point sources from samples of their convolution with a Gaussian kernel, showing that a convex program achieves exact deconvolution as long as the sources are not too clustered together and there are at least two samples close to the location of each source. The result is established using a novel dual-certificate construction.

Original languageEnglish (US)
Title of host publication2017 12th International Conference on Sampling Theory and Applications, SampTA 2017
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages60-63
Number of pages4
ISBN (Electronic)9781538615652
DOIs
StatePublished - Sep 1 2017
Event12th International Conference on Sampling Theory and Applications, SampTA 2017 - Tallinn, Estonia
Duration: Jul 3 2017Jul 7 2017

Other

Other12th International Conference on Sampling Theory and Applications, SampTA 2017
CountryEstonia
CityTallinn
Period7/3/177/7/17

Fingerprint

Sampling Theorem
Deconvolution
Point Source
Convolution
Sampling
Gaussian Kernel
Convex Program
Certificate

ASJC Scopus subject areas

  • Signal Processing
  • Statistics, Probability and Uncertainty
  • Analysis
  • Statistics and Probability
  • Applied Mathematics

Cite this

Bernstein, B., & Fernandez-Granda, C. (2017). A sampling theorem for deconvolution of point sources. In 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017 (pp. 60-63). [8024426] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/SAMPTA.2017.8024426

A sampling theorem for deconvolution of point sources. / Bernstein, Brett; Fernandez-Granda, Carlos.

2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. Institute of Electrical and Electronics Engineers Inc., 2017. p. 60-63 8024426.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bernstein, B & Fernandez-Granda, C 2017, A sampling theorem for deconvolution of point sources. in 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017., 8024426, Institute of Electrical and Electronics Engineers Inc., pp. 60-63, 12th International Conference on Sampling Theory and Applications, SampTA 2017, Tallinn, Estonia, 7/3/17. https://doi.org/10.1109/SAMPTA.2017.8024426
Bernstein B, Fernandez-Granda C. A sampling theorem for deconvolution of point sources. In 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. Institute of Electrical and Electronics Engineers Inc. 2017. p. 60-63. 8024426 https://doi.org/10.1109/SAMPTA.2017.8024426
Bernstein, Brett ; Fernandez-Granda, Carlos. / A sampling theorem for deconvolution of point sources. 2017 12th International Conference on Sampling Theory and Applications, SampTA 2017. Institute of Electrical and Electronics Engineers Inc., 2017. pp. 60-63
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